Investigation of the application of statistical analysis tools to commercial aircraft engine performance and design

This thesis is an investigation of the use of a statistical sampling code and a regression analysis code to develop a simple mathematical function that represents the relationship between a given engine's thrust and its operating parameters. The analysis has direct application to the general design and performance analysis of commercial aircraft engines. The statistical sampling code was written by Department of Energy personnel. It employs a Latin Hypercube sampling (LHS) technique which permits accurate sampling of engine behavior over an input parameter list while using a minimum amount of data. The regression analysis code (STEP) yields information on engine parameter interrelationships, and was used to perform multivariate regression analysis. Two thermodynamic cycle decks were also used in this investigation in order to obtain the thrust values of a specific airbreathing engine operating at specified flight conditions. These cycle decks, written by faculty of the United States Air Force Academy, address on-design (ONX) and off-design (OFFX) engine behavior. All of the codes used in this thesis are publicly available with unlimited distribution. The representative scenario that was chosen for this thesis was the determination of the change in takeoff thrust of a specific engine at a variety of airport elevations and over a range of ambient temperatures. This type of scenario provided important information concerning the upper limit of temperature that will safely permit takeoff from a given airport. First, the LHS program was used to obtain the sample set of takeoff conditions (altitudes and temperatures). In order to obtain engine performance data, the ONX and OFFX programs were then exercised at the conditions specified by LHS. Finally, the regression analysis was conducted using STEP in order to determine a mathematical function that expressed takeoff thrust for the given engine at any elevation and temperature. A comparison is presented for engine math model (i.e., cycle deck) data vs. the thrust predicted by the function derived from LHS and STEP. The main conclusion of the research was that remarkably accurate functional relations could be achieved using LHS and STEP. A suitable amount of background theory is included for the computational methods underlying each code. The results of the application of these programs showed that they represent useful, viable tools for the investigation of the performance of aircraft engines, and that they do so in a manner that legitamitely permits the use of a minimal amount of data via the Latin Hypercube sampling technique. As the costs increase to obtain today's engineering test data (or model predictions), so does the importance of the application of such methods, because they permit fewer tests to be performed in order to obtain a predictive operational database.